A163942 Fifth right hand column of triangle A163940.

1, 14, 121, 834, 5037, 27918, 145777, 728858, 3526933, 16640262, 76952793, 350167122, 1572467389, 6984206846, 30735634369, 134202204426, 582040933605, 2509672804470, 10766469841705, 45982221941570, 195609944400781

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.

Index entries for linear recurrences with constant coefficients, signature (14,-75,190,-224,96).

Formula

G.f.: 1/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)^2).

a(n) = (1/18)*(3^(n+6) + (3*n-10)*4^(n+3) - 9*2^(n+3) + 1).

a(n) = 14*a(n-1) - 75*a(n-2) + 190*a(n-3) - 224*a(n-4) + 96*a(n-5).

E.g.f.: (1/18)*( 729*exp(3*x) + 128*(6*x-5)*exp(4*x) - 72*exp(2*x) + exp(x)). - G. C. Greubel, Aug 13 2017

Mathematica

CoefficientList[Series[1/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2017 *)
LinearRecurrence[{14, -75, 190, -224, 96}, {1, 14, 121, 834, 5037}, 30] (* Harvey P. Dale, Mar 09 2023 *)

Prog

(PARI) Vec(1/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)^2) + O(x^30)) \\ Michel Marcus, Feb 12 2015

Crossrefs

Equals the fifth right hand column of A163940.

A163941 is another right hand column.

Sequence in context: A002056 A249980 A206635 * A206628 A370966 A235710

Adjacent sequences: A163939 A163940 A163941 * A163943 A163944 A163945

Keyword

easy,nonn

Author

Johannes W. Meijer, Aug 13 2009

Status

approved